The interest on Rs. 300 for 5 years is Rs. 37.50. What will be the interest on Rs. 100 for the same years?​

i. Cube of any odd number is even. False

ii.  A perfect cube does not end with two zeros. True

iii.  If square of a number ends with 5, then its cube ends with 25. False

iv. There is no perfect cube which ends with 8. False

v. The cube of a two digit number may be a three digit number. False

vi.  The cube of a two digit number may have seven or more digits. False

vii. The cube of a single digit number may be a single digit number. True

i.  Cube of any odd number is even. This statement is false because the cube of odd numbers are also odd

ii.  A perfect cube does not end with two zeros. This statement is True because the cube of a two digit number cannot be a 3 digit number and therefore cannot end with two zeros.

iii.  If square of a number ends with 5, then its cube ends with 25. This statement is False

Using the illustration

35^2 = 35 x 35= 1225 , its square ends with 5

35^3= 35 x 35 x 35= 42875 which ends with 75

iv.  There is no perfect cube which ends with 8. This statement is False.

Using the illustration, the cube of 2 is given thus

2 * 2 * 2 = 8

The cube of 2 ends with 8

v. The cube of a two digit number may be a three digit number. This statement is False.

Using the illustration, 10 is a two digit number

10 * 10 * 10 = 1000

The cube of 10 which is a two digit number is not a three digit number and same applies to all two digit numbers

vi  The cube of a two digit number may have seven or more digits. This statement is False because the cube of a two digit number can only be a four digit number.

vii. The cube of a single digit number may be a single digit number. This statement is True because the cube of a single digit number can be a single, two or three digit number.

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Using an exponential function, it is found that the half-life of the substance is of 5.23 units of time.

The function is given by:

[tex]A(t) = A(0)e^{-kt}[/tex]

In which:

The parameters are given by:

A(0) = 48,  k = 0.1325.

Hence the equation is:

[tex]A(t) = 48e^{-0.1325t}[/tex]

The half-life is the amount of time for which A(t) = 0.5A(0) = 24, hence:

[tex]A(t) = 48e^{-0.1325t}[/tex]

[tex]24 = 48e^{-0.1325t}[/tex]

[tex]e^{-0.1325t} = 0.5[/tex]

[tex]\ln{e^{-0.1325t}} = \ln{0.5}[/tex]

[tex]0.1325t = -\ln{0.5}[/tex]

[tex]t = -\frac{\ln{0.5}}{0.1325}[/tex]

t = 5.23.

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It is to be noted that the Graph of the indicated inequalities is herewith attached.

As indicated above, this is a graph of a system of inequalities, where:

Y > -4x-1 and

y <3/2x-1

No. the point (-1, 1) is not included in the solution area for the system.

Step 1 - Plug in (-1, 1) in to the first equation. where y = -1 and x = 1.

Hence,

-1 > -4(1) -1

4 +1 < -1

4 < 0 (This is False)

Step 2  - Plug in (-1, 1) in to the second equation. where y = -1 and x = 1.

-1 < (3/2)(1) - 1

-1 < 1/2 (This is true).

Thus (-1, 1) is only partially included in the solution area.)

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The decision when the z value is within the rejection region is that we'll have to reject the null hypothesis.

It should be noted that the rejection region is also known as the critical region. It is the set of values where the null hypothesis is rejected.

When the observed test statistic is in the rejection region, we'll have to reject the null hypothesis and then accept rte alternative hypothesis.

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The equation representing the value of the collection after 7 years is  value of collection = 430 + (0.04 * 430 )* 7 or value of collection = $550.4

An equation is a mathematical statement , where the algebraic expression is equated to another algebraic expression.

It is given that

Ella has a collection of vintage action figures that is worth $430.

collection

appreciates at a rate of 4% per year

equation representing the value of the collection after 7 years is

value of collection = 430 + (0.04 * 430 )* t

value of collection = 430 + (0.04 * 430 )* 7

= $550.4

Therefore the equation representing the value of the collection after 7 years is  value of collection = 430 + (0.04 * 430 )* 7 or value of collection = $550.4

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Answer: A

Step-by-step explanation:

[tex]\frac{dy}{dx}=\frac{1+x}{xy} \\ \\ y \text{ } dy=\frac{1+x}{x} \text{ } dx \\ \\ y \text{ } dy= \left(\frac{1}{x}+1 \right) \text{ } dx \\ \\ \int y \text{ } dy=\int \left(\frac{1}{x}+1 \right) \text{ } dx \\ \\ \frac{y^{2}}{2}=\ln \left| x \right|+x+C[/tex]

Substituting in the initial condition,

[tex]\frac{(-2)^{2}}{2}=\ln \left|1 \right|+1+C\\\\2=1+C\\\\C=1[/tex]

So,

[tex]\boxed{\frac{1}{2}y^{2}=\ln \left|x \right|+x+1}[/tex]

Answer:

[tex]\textsf{A.} \quad \dfrac{1}{2}y^2=\ln|x|+x+1[/tex]

Step-by-step explanation:

To solve the differential equation:

Rearrange the given equation to get all the terms containing y on the left side, and all the terms containing x on the right side:

         [tex]\dfrac{dy}{dx}=\dfrac{1+x}{xy}[/tex]

[tex]\implies y\dfrac{dy}{dx}=\dfrac{1+x}{x}[/tex]

[tex]\implies y\:dy=\dfrac{1+x}{x}\:dx[/tex]

[tex]\implies y\:dy=\dfrac{1}{x}+\dfrac{x}{x}\:dx[/tex]

[tex]\implies y\:dy=\left(\dfrac{1}{x}+1\right)\:dx[/tex]

Integrate both sides:

[tex]\displaystyle \implies \int y\:dy=\int \left(\dfrac{1}{x}+1\right)\:dx[/tex]

[tex]\implies \dfrac{1}{2}y^2=\ln|x|+x+C[/tex]

Find the value of C using the given values of x and y:

when x = 1, y = -2

[tex]\implies \dfrac{1}{2}(-2)^2=\ln|1|+1+C[/tex]

[tex]\implies 2=0+1+C[/tex]

[tex]\implies C=1[/tex]

Substitute the found value of C:

[tex]\implies \dfrac{1}{2}y^2=\ln|x|+x+1[/tex]

Answer:

x = 10

Step-by-step explanation:

5(2x - 12) + 21 = 2x + 41 ← distribute parenthesis and simplify left side

10x - 60 + 21 = 2x + 41

10x - 39 = 2x + 41 ( subtract 2x from both sides )

8x - 39 = 41 ( add 39 to both sides )

8x = 80 ( divide both sides by 8 )

x = 10

The line is drawn at point A and Point C is a line of symmetry because lines of symmetry make exactly two halves with similar shapes and sizes.

It is defined as the line which will make exactly two halves with similar shape and size in geometry. For a two-dimensional shape, there is a line of symmetry, and for three-dimensional shapes, there is a plane of symmetry. In other words, if we make a mirror image of the shape around the line of symmetry, we will get exactly the same half portion.

We have given a figure in the picture.

The figure is a quadrilateral(a kite)

As we know, lines of symmetry make exactly two halves with similar shapes and sizes.

IF we draw a line from Point A to Point C we will get two similar and figures in size and shape.

Thus, the line is drawn point A and Point C is a line of symmetry because lines of symmetry make exactly two halves with similar shapes and sizes.

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Answer:

point C

Here is a step-by-step explanation of the statement:

1. Draw a point B and a point C on a piece of paper or a computer screen.

2. Draw a straight line that goes through both point B and point C.

3. Fold the paper along the line you just drew, so that the line is the fold line.

4. Notice that if you were to fold the paper exactly in half along the line, point B would match up with its reflection on the other side of the line, and point C would match up with its reflection on the other side of the line.

5. This means that the line you drew is a line of symmetry, because it divides the paper into two identical halves that can be folded together.

6. Therefore, the statement "A line drawn through point B and point C is a line of symmetry" is true.

Answer #1:

The total cost with 6 snacks is $78.

Answer #2:

The total cost with x snacks is represented by the expression 60 + 3x.

Step-by-step explanation for answer #1:

Starting off with what we know:

To answer the question of how much money Genesis would have to pay for her family if she bought 6 snacks for everybody, first consider the total cost of the movie tickets.

Multiply the total number of people by the cost of each movie ticket:

[tex]4* 15=60[/tex]

Genesis will be paying $60 total only to see the movie with her 3 kids. To find the total cost of both seeing the movie and buying 6 snacks, simply multiply the number of snacks by the cost of each snack:

[tex]6 * 3=18[/tex]

Then, add the total cost of the movie tickets by the total cost of the snacks to achieve your first answer:

[tex]60+18=78[/tex]

The total cost with 6 snacks is $78.

Step-by-step explanation for answer #2:

To find the total cost of "x" snacks (x is being used as a variable term to represent a quantity subject to change), we can create an algebraic expression.

Let "t" represent the total cost.

Since we've established that finding the total cost is just a matter of adding the total cost of movie tickets (60) and the total cost of snacks (3 multiplied by the number of snacks), let "x" represent the number of snacks in the equation to find the total cost with x snacks:

[tex]60+3x=t[/tex]

The total cost with x snacks is represented by the expression 60 + 3x.

Based on the given data, the total cost of 6 snacks: $78. total cost with x snacks: $60 + (3x).

Use the concept of multiplication defined as:

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that,

Genesis is going to see a movie with her 3 kids.

Each movie ticket costs $15.

There are snacks available for purchase at $3 each.

Genesis wants to buy 6 snacks for everybody to share.

To calculate the total cost for Genesis and her 3 kids,

Consider the movie tickets and the snacks.

The cost of the movie tickets can be calculated by multiplying the number of people (4 in this case) by the cost of each ticket ($15).

So, Genesis would have to pay 4 x $15 = $60 for the movie tickets.

Now, let's calculate the total cost if Genesis were to buy 6 snacks for everybody to share.

Each snack costs $3, so 6 snacks would cost 6 x $3 = $18.

Therefore, the total cost for Genesis would be,

$60 (movie tickets) + $18 (snacks) = $78.

If we consider x snacks for everybody to share,

The total cost for snacks would be x $3.

So, the final cost would be $60 (movie tickets) + (3x) (snacks).

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Answer:

240

Step-by-step explanation:

Using the straight line formula; y=mx+c, take two points, for example, (4, 80) and (5, 100)

m=change in y/change in x, so;

m=(100-80)/(5-4)= 20

Take point (4, 80)

80=20×4 + c

80-80=c=0

so y=20x

y=20×12=240

The value of x is 10√3 .

The missing figure is attached with the answer

A triangle is a polygon with three sides , three angles and three vertices.

A right angle is a triangle in which one of the sides of a triangle is equal to 90 degree.

As it is a right angled triangle therefore the trigonometric ratios are applicable

From the given figure sin 60 needs to be determine to find the value of x

sin x = Perpendicular / Hypotenuse

sin 60 = 5 / x

[tex]\rm \dfrac{\sqrt{3}}{2} = \dfrac{5}{x}[/tex]

x = 10√3

Therefore the value of x is 10√3

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Answer:

[tex]IK = IJ\sqrt{2}[/tex]

Step-by-step explanation:

First, it's an isosceles right triangle, which means there is a 90 degree angle and the two other angles are equal.

To find what the two other angles are, you can set up a quick equation:

let x be angle

90 + 2x = 180, since the sum of the interior angles in a triangle is always 180.

then,

[tex]2x = 90\\x = 45[/tex]

Therefore, the triangle is a 45-45-90 triangle.

You have the measure of IJ, which is one of the legs of the triangle. The way you can find the length of the hypotenuse of a 45-45-90 triangle is by multiplying the length of one of the legs by [tex]\sqrt{2}[/tex].

This means the equation is [tex]IK = IJ\sqrt{2}[/tex]

Answer:

[tex]\sf IK=IJ\sqrt{2}[/tex]

Step-by-step explanation:

The interior angles of a triangle sum to 180°.  Therefore, if ΔIJK is an isosceles right triangle where m∠J = 90°:

To calculate the base angles:

⇒ m∠K + m∠I + m∠J = 180°

⇒ m∠K + m∠I + 90° = 180°

⇒ m∠K + m∠I = 90°

⇒ m∠K = m∠I = 45°

Therefore, IJ and JK are the legs of the right triangle and IK is the hypotenuse.

To find the length of the hypotenuse, use Pythagoras' Theorem.

Pythagoras’ Theorem:  [tex]\sf a^2+b^2=c^2[/tex]

(where a and b are the legs, and c is the hypotenuse, of a right triangle)

Given:

Substitute the given values into the formula and solve for IK:

[tex]\sf \implies IJ^2+JK^2=IK^2[/tex]

[tex]\sf \implies 4^2+4^2=IK^2[/tex]

[tex]\sf \implies IK^2=32[/tex]

[tex]\implies \sf IK=\sqrt{32}[/tex]

[tex]\implies \sf IK=\sqrt{16 \cdot 2}[/tex]

[tex]\implies \sf IK=\sqrt{16}\sqrt{2}[/tex]

[tex]\implies \sf IK=4\sqrt{2}[/tex]

As IJ = 4 then:

[tex]\implies \sf IK=IJ\sqrt{2}[/tex]

[tex]\log_290=\log_2(3^2\cdot10)=\log_23^2+\log_210=2\log_23+b=2a+b[/tex]

Answer:

[tex]-4^{15}[/tex]

Step-by-step explanation:

Given expression:

[tex]\left[(-4)^5\right]^3[/tex]

[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]

[tex]\implies (-4)^{(5 \times 3)}[/tex]

[tex]\implies (-4)^{15}[/tex]

[tex]\textsf{Apply exponent rule} \quad (-a)^n=-a^n,\:\: \textsf{ if }n \textsf{ is odd}:[/tex]

[tex]\implies -4^{15}[/tex]

Answer:

x-intercept: -4

Step-by-step explanation:

It's where the slope intercepts with the x-axis

Answer:

Step-by-step explanation:

x-intercept:  the x-value is that when y = 0:  (-4, 0).

y-intercept:  the y-value when x = 0: (0, 5)

Step-by-step explanation:

[tex]z - 6 < 3 \\ z < 3 + 6 \\ z < 9[/tex]

Hope it helps

Z – 6 < 3

Z < 3 + 6

Z < 9

Answer:

“The slope is Negative three-fourths, and the y-intercept is 3.”

Step-by-step explanation:

the graph passes through the points (0 , 3) and (4 , 0)

Then

The slope is :

[tex]=\frac{0-3}{4-0}[/tex]

[tex]=-\frac{3}{4}[/tex]

Since , the graph passes through (0 , 3)

THen the y-intercept is 3.

Step-by-step explanation:

[tex] = 4x - 8y + 6 {x}^{2} + 3x - 5y[/tex]

[tex] = 6 {x}^{2} + (4x + 3x) + ( - 8y - 5y)[/tex]

[tex] = 6 {x}^{2} + 7x - 13y[/tex]

The answer is B.

Answer:

b.) 6x² + 7x - 13y

Explanation:

Given Expression

= 4x - 8y + 6x² + 3x - 5y

collect like terms

= 6x² + 4x + 3x -8y - 5y

combine similar terms

= 6x² + 7x - 13y

At first, he made [tex]2\frac{5}{8}[/tex] kg of tuna filling.

Mr Abdul made tuna and curry potato filling for some puffs.

3/5 of the filling he made was tuna and the rest was curry potato.

So, amount of curry potato = 1- 3/5 = 2/5

Ratio of tuna & curry potato = tuna : curry potato

                                               = 3/5 : 2/5  = 3 : 2

Let amount of tuna = 3x & amount of curry potato = 2x

After he used 1/8kg of the tuna filling and made another 3/4 kg of curry potato filling.

According to the question, he then had equal amounts of tuna filling and curry potato filling left.

So, 3x - 1/8 = 2x + 3/4

Multiplying 8 in both sides we get,

⇒ 24x - 1 = 16x +6

⇒ 24x - 16x = 7

⇒ 8x = 7

⇒ x = 7/8

So, 3x = (3×7/8) = 21/8 kg = [tex]2\frac{5}{8}[/tex] tuna filling at first.

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Answer:

the graph of f(x)= -2-10x+16

Answer:

the vertex would be (-5,41)

Step-by-step explanation:

You just plug the -5 back into the equation to get 41

Divya should not check her answers for extraneous solution as it's not required in this case.

It should be noted that an extraneous solution simply means is the transformed equation that's isn't the root of the original equation.

Based on the information given, Divya had already solved the equation and it's not necessary to check the answers for extraneous solution.

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Answer:

No, she shouldn't.

Answer:

The boy earned $773 in the fourth month.

Step-by-step explanation:

1) First, we need to find the total amount of money he needs so that the average of the 4 months would be 500. We can do this by multiplying 500 and 4 (essentially, we are working backward when trying to find the average) [tex]500*4=2000[/tex] So, we know that the boy needs $2000 total by the end of the fourth month to make the 4-month average $500.

2) Now, we know how much the boy made for the first 3 consecutive months, so add those numbers up. [tex]435+230+562=1227[/tex] So within the first 3 months, the boy made $1227.

3) Finally, we know how much money the boy needs by the end of the fourth month and how much he made by the third, so to figure out how much he earned in the fourth month, we can simply subtract $1227 from $2000. [tex]2000-1227=773[/tex]

There 6840 ways  can first, second, and third place be assigned.

A permutation is a mathematical technique that determines the number of possible arrangements in a set when the order of the arrangements matters.

We will use the concept of permutation

[tex]^{20}P_3[/tex]= 20!/ (20-3)!

     = 20*19*18*17!/ 17!

    = 6840 ways.

Hence, there are 6840 ways.

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Answer:

cos65 = sin25 = p

tan205 = tan25 = p/√(1-√p)

Step-by-step explanation:

trigonometry, the branch of mathematics concerned with specific functions of angles and their application to calculations. There are six functions of an angle commonly used in trigonometry. Their names and abbreviations are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (cosec)

some Trigonometric identities used in the question:

in the question it is given,

sin25 = p

using above mentioned identity:-

cos 65 = cos(90-25) = sin25 = p

hence value of cos65 is p.

for, tan205 we have to first find the cos25

so to find cos25 we use above mentioned identity,

cos²25 + sin²25 = 1

cos²25 + √p      = 1

cos²25               = 1-√p

cos25               = √(1-√p)  

now to find out tan205 use third identity mentioned above,

tan205 = tan(π+25) = tan25

tan25 = sin25/cos25

tan25 = p/√(1-√p)  

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Answer:

Step-by-step explanation:

30 is an opposite angle (2 angles of 30°)

sum of all angles = 360°

360 - 90 -30 - 150 - 30 = 60°

check

60 + 30 + 150 + 30 + 90 = 360°

the answer is good

Answer:

b = 60

Step-by-step explanation:

A straight line is 180 degrees

30+90+b = 180

Combine like terms

120 +b = 180

b =180-120

b = 60

Answer:

(f+g)(x)

= |3x+5| + 13

Step-by-step explanation:

(f+g)(x) means

f(x) + g(x)

so you add the functions together.

|3x+5| + 6 + 7

And simplify.

|3x+5| + 13

Answer:

The choice D.

[tex]f(x) = 3 {(0.2)}^{x} [/tex]

Answer:

D

Step-by-step explanation:

Order of elimination:

1. the graph is going down exponentially. This means that the base is less than 1.

A and C are eliminated.

2. When x is equal to 0, f(x) = 3.

Substitute x for 0, and you'll find out that the only one possible is D.

Answer:

a) The third term is 19
b) The new term-to-term rule is subtract 13 and then divide by 6.

Step-by-step explanation:

First term: -2
Second term: 1 (-2 * 6 = -12 + 13 = 1)
Third term: 19 (1 * 6 = 6 + 13 = 19)

Our reversed sequence is now 19, 1, -2

First term: 19

Second term: 1 (19 - 13 = 6 / 6 = 1)

Third term: -2 (1 - 13 = -12 / 6 = -2)

It's term is -3 it can be divided into 6 points +79

The provided equation has no solution because the square of any number cannon is negative.

It is defined as the combination of constants and variables with mathematical operators.

The question is incomplete.

The complete question is:

Find a solution to the given equation

Please refer to the attached picture for the expression.

We have an expression:

[tex]\rm \dfrac{3}{\left(m+3\right)}-\dfrac{3}{\left(m-3\right)}=\dfrac{m^2+9}{\left(m^2-9\right)}[/tex]

3(m - 3) - 3(m + 3) = m² + 9

3m - 9 - 3m - 9 = m² + 9

m²  ≠ -27

As the square of any number cannot is negative, so no solution to the provided equation.

Thus, the provided equation has no solution because the square of any number cannon is negative.

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Answer:

D = No Solution

Step-by-step explanation: